Question 1128413: A park has two sprinklers that are used to fill a fountain. One sprinkler can fill the fountain in 4 h, whereas the second sprinkler can fill the fountain in 12 h. How long will it take to fill the fountain with both sprinklers operating?
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13196)   (Show Source):
You can put this solution on YOUR website!
The classic way to solve this kind of problem is to think of the fractions of the job each sprinkler does in one hour.
In this problem, one sprinkler fills 1/4 of the fountain in 1 hour and the other fills 1/12 of it in one hour. Together, then, the fraction of the fountain they fill is
Then, since together they fill 1/3 of the fountain in one hour, it takes them 3 hours to fill to fountain.
This is a very common problem that I see frequently on high school math competition tests. An experienced student will just write down the answer without having to do much work at all; the answer is just "product divided by sum" -- in this problem,  .
Here is how that works in general....
Suppose the two times for the two workers are x and y. Then the fractions they do in one unit of time are 1/x and 1/y. The fraction they do together in one unit of time is 1/x+1/y = (x+y)/(xy); then the amount of time they take to do the job together is the reciprocal of that number, which is (xy)/(x+y).
There is also another easy alternative method for solving this type of problem that many students like.
Consider the least common multiple of the two times for the two sprinklers; the LCM of 4 and 12 is 12.
Now imagine each sprinkler working for 12 hours. The one that can fill the fountain in 4 hours could fill the fountain 3 times in 12 hours; the one that can fill it in 12 hours could fill the fountain 1 time in 12 hours.
Together, then, they could fill the fountain 4 times in 12 hours; that means they could fill it once in 3 hours.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! A park has two sprinklers that are used to fill a fountain. One sprinkler can fill the fountain in 4 h, whereas the second sprinkler can fill the fountain in 12 h. How long will it take to fill the fountain with both sprinklers operating?
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The "4 hour" sprinkler is equivalent to 3 12 hour sprinklers.
= 4 of the 12 hour sprinklers
---> 3 hours to fill the fountain.
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